Question

A boys spends $\frac{3}{4}$ of his pocket money and then $4$ by $5$ of the reminder is given to his sister if he has rupees $40$ left, what did you have at first?

Answer 1

Let the pocket money be $=x$
$x-\frac{3x}{4}$ is amount remaining with him after spending money.
$x-\frac{3x}{4}=\frac{4x-3x}{4}$
$\Rightarrow x-\frac{3x}{4}=\frac{x}{4}$
Now, he gave $\frac{4}{5}$ of remaining amount to his sister.
then the remaining amount is $\frac{x}{4}-\frac{4}{5}\times \frac{x}{4}$
$=\frac{x}{4}-\frac{x}{5}$
$=\frac{5x-4x}{20}$
$=\frac{x}{20}$
According to given question remaining amount is $40$
Thus, $\frac{x}{20}=40$
$\Rightarrow x=40\times 20$
$\therefore x=800$
His pocket money is $800$